A top Republican fundraiser close to President Donald Trump was in negotiations to earn tens of millions of dollars if the U.S. Justice Department dropped its investigation into a multibillion-dollar graft scandal involving a Malaysian state investment fund, according to emails reviewed by The Wall Street Journal.

In emails dated during the past year, Elliott Broidy, a venture capitalist and a longtime Republican donor, and his wife, Robin Rosenzweig, an attorney, discuss setting up a consulting contract with Jho Low, the...